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Least‐square collocation and Lagrange multipliers forTaylor meshless method
Author(s) -
Yang Jie,
Hu Heng,
PotierFerry Michel
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22287
Subject(s) - collocation (remote sensing) , piecewise , mathematics , lagrange multiplier , constraint algorithm , square (algebra) , taylor series , collocation method , orthogonal collocation , regularized meshless method , boundary value problem , polynomial , boundary (topology) , lagrange polynomial , mathematical analysis , singular boundary method , differential equation , mathematical optimization , geometry , computer science , ordinary differential equation , boundary element method , finite element method , physics , machine learning , thermodynamics
A recently proposed meshless method is discussed in this article. It relies on Taylor series, the shape functions being high degree polynomials deduced from the Partial Differential Equation (PDE). In this framework, an efficient technique to couple several polynomial approximations has been presented in (Tampango, Potier‐Ferry, Koutsawa, Tiem, Int. J. Numer. Meth. Eng . vol. 95 (2013) pp. 1094–1112): the boundary conditions were applied using the least‐square collocation and the interface was coupled by a bridging technique based on Lagrange multipliers. In this article, least‐square collocation and Lagrange multipliers are applied for boundary conditions, respectively, and least‐square collocation is revisited to account for the interface conditions in piecewise resolutions. Various combinations of these two techniques have been investigated and the numerical results prove their effectiveness to obtain very accurate solutions, even for large scale problems.